Tag: 2075 Entrance Exam

We known,

Surface tension =𝐹/L = [𝑀^1 𝐿 𝑇 ^−2]/ [L] = [M𝑇^−2]

Hence, the correct answer is option d. [M𝑇^−2]

Given,

Force(F)=5N

weight(w)= 10 N

Acceleration due to gravity(g)=9.8 m/s^2

$W=mg$,  where g=9.8 m/s^2

10 = m x 9.8

m= 10/9.8

using F=ma,

a= F/m = 5/(10/9.8 ) ≈5m/s^2.

Hence, the correct answer is option c. 5m/s^2.

Acceleration due to gravity become half (g′)=g/2,

The acceleration due to gravity at depth $d$ is given by:

g′=g(1−d/R).

g/2 = g(1−d/R)

on solving,

d=R/2.

Hence, the correct answer is option c. d=R/2

Spokes increase the moment of inertia of the wheel by distributing the mass farther from the axis of rotation, making the wheel more stable and easier to balance.

Hence, the correct answer is option c. increase moment of inertia

Young’s modulus is a material property and is independent of the dimensions of the wire. It remains constant regardless of changes in length or diameter.

Hence, the correct answer is option c. remain same

Given,

radius(r)= 0.3 mm = 0.3×10^−3

velocity(v)= 1 m/s

viscosity of air(η)=18×10^−5

The viscous force F is given by Stokes’ law:

$F=6\pi \eta rv$, where η is the viscosity, $r$ is the radius, and $v$ is the velocity.

=6×3.14×18×10^−5×0.3×10^−3×1≈1.01×10^−8N.

Hence, the correct answer is option b. 1.01×10^−8N

Invar is an alloy known for its extremely low coefficient of thermal expansion, making it ideal for applications requiring dimensional stability over a range of temperatures.

Hence, the correct answer is option b. invar

Lets say of volume ‘V’ it is at 27°C . converting Celsius to kelvin we get 300K , this is what almost all workings contain.

now we say that 1/4th of the air is expelled, due to the expansion. but does this mean that this expelled air creates a vacuum in the flask? NO. so basically the place is taken by the air left in the flask which has expanded. now just for the sake of visualisation, lets consider the absence of the flask and the presence of this air in vacuum. so we said that 1/4th of V is out , but the remaining 3/4th is still in the flask but due to expansion it covers V volume. so now the total volume air present in total is V+1/4V =5/4V.

now using the basic gas laws we can say,

V1/T1=V2/T2

V/T=(5/4V)/T

V/300=(5/4V)/T

V and V cancel and we are left with the equation T=(5/4)*300

therefore T=375K, which 102°C

Hence, the correct answer is option c. 102°C

According to the Carnot efficiency equation,

η=1− Tc/ Th where Tc​ is the temperature of the sink and Th​ is the temperature of the source. The efficiency can only reach 100% if Tc=0K.

Hence, the correct answer is option a. 0K.​

Given,

emissivity(ε) = 1 (since we are not given),

Stefan-Boltzmann constant(σ )= 6 × 10⁻⁸ W/m²-K⁴,

Surface area of cylindrical wall heater(A) = 2πrh where

radius of wall heater(r) = 6 mm = 6 × 10⁻³ m and

length of heater(h) = 0.6 m, and

Temperature of heater(T)=?

Since P = εσAT⁴

P = εσ(2πrh)T⁴

Making T subject of the formula, we have

Temperature of heater

T = ⁴√[P/εσ(2πrh)]

Since P = 1.5 kW = 1.5 × 10³ W

Substituting the values of the variables into the equation, we have

T = ⁴√[P/εσ(2πrh)]

T = ⁴√[1.5 × 10³ W/(1 × 6 × 10⁻⁸ W/m²-K⁴ × 2π × 6 × 10⁻³ m × 0.6 m)]

T = ⁴√[1.5 × 10³ W/(43.2π  × 10⁻¹¹ W/K⁴)]

T = ⁴√[1.5 × 10³ W/135.72  × 10⁻¹¹ W/K⁴)]

T = ⁴√[0.01105 × 10¹⁴ K⁴)]

T = ⁴√[1.105 × 10¹² K⁴)]

T = 1.0253 × 10³ K

T = 1025.3 K

Hence, the correct answer is option c. 1025K

Given

angular position of second minima(m)=2

wavelength(λ)=  550 nm = 550×10^−9 m

we known,

sinθdan=mλ/d

sinθdan=2×550×10^−9/22×10^−7

$\theta ={\mathrm{30°}}^{}$

Hence, the correct answer is option b. ${\mathrm{30°}}^{}$

The power $P$ of a lens is the reciprocal of the focal length f in meters: P=1/f​. When two lenses are placed in contact, their powers add algebraically:

Peq​=P1​+P2​=5D+(−7.5D)=−2.5D

The equivalent focal length feq​ is:

feq​=1/Peq​​=1/−2.5D​=−0.4m=−40cm

Hence, the correct answer is option a. −40cm

$L_{\infty }=v_0+f_e\Rightarrow 14=v_0+5\Rightarrow v_0=9cm$

Magnifying power of microscope for relaxes eye

$m=(\frac{v_{\mathrm{0/}}}{u_{\mathrm{0)\; x\; (}}}\frac{\mathrm{D/}}{f_{\mathrm{e)}}}$

or $25=(\frac{\mathrm{9/}}{u_{\mathrm{0)}}}.(\frac{\mathrm{25/}}{\mathrm{5)}}$

or $u_0=\frac{\mathrm{9/}}{5}=1.8cm$

Hence, the correct answer is option d. $1.8cm$

The distance between two points i.e. path difference between them

Electrostatic potential energy between two like charges (both negative, like electrons) is positive and increases as the charges are brought closer together due to the repulsive force between them.

Hence,the correct answer is option b. increases

When capacitors are connected in series, the equivalent capacitance decreases and is given by Cs=C/n. When they are connected in parallel, the equivalent capacitance increases and is given by Cp=nC. The ratio of maximum (parallel) to minimum (series) capacitance is:

Ratio=Cp/Cs ​​​= (nC)/(​n/C)​ = n^2

Hence, the correct answer is option a. n^2

When the wire is bent into a circle, it forms two equal resistances in parallel. Each half has a resistance of 6 Ω. The effective resistance between two diametrically opposite points (points on a diameter) is given by:

1/R​=(1/6Ω​)+(1/6Ω)=2/6Ω

R=6Ω/2 =3Ω

Hence, the correct answer is option d. 3Ω

An ideal ammeter has zero resistance so that it does not affect the current it is measuring.

Hence, the correct answer is option a. 0

Given,

Kinetic energy of electron ( $\frac{\mathrm{1\; mv^2/}}{2}$ ) = 10 eV = 1$0\times (1.6\times {\mathrm{10^}}^{-19})$ J

Magnetic induction (B) = ${\mathrm{10^}}^{-\mathrm{4\; T}}$

orbital radius of electron(r)=?

mass of electron= $9.1\times {\mathrm{10^}}^{-31}$Kg

(9.1×10^−31)v^2 x 1/2=10×(1.6×10^−19)

${\mathrm{v^}}^2$= $3.52\times {\mathrm{10^}}^{12}$

v = $1.876\times {\mathrm{10^}}^6$ m

Now centripetal force = mv^2 / r = Bev

Therefore, r= mv/Be = (9.1×10^−31×1.876×10^6)/(10^−4×1.6×10^−19)

r= $11\times {\mathrm{10^}}^{-2}$ m = 11 cm

Hence, the correct answer is option c. 11 cm

According to Faraday’s Law, the emf is induced as long as there is a change in magnetic flux.

Hence, the correct answer is option d. so long as the change in flux takes place

Retentivity is the ability of a material to retain magnetization after the external magnetic field is removed. This property is crucial for making permanent magnets.

Hence, the correct answer is option a. permanent magnet

The color of the light emitted in a gas discharge tube depends on the type of gas used, as different gases emit different colors when excited.

Hence, the correct answer is option c. the gas in the tube

According to the photoelectric effect, the kinetic energy of the emitted electrons depends on the frequency of the incident light, not the intensity.

Hence, the correct answer is option a. frequency

Power of nuclear reactor $=16KW$

Energy per fission $=200MeV$

No of fissions per second $=(16\times 10^3)/($$\frac{200\times {\mathrm{10^}}^6\times 1.6\times {\mathrm{10^}}^{-\mathrm{19)\; =\; 5\; x\; 10^14}}}{}$

Hence, the correct answer is option d. $\frac{{}^{}}{}$

P-type semiconductors are obtained by doping silicon with a trivalent element like aluminum, which creates holes as charge carriers.

Hence, the correct answer is option a. aluminum

The mass of one hydrogen atom is approximately 1.67 × 10^-24 grams.

Hence, the correct answer is option c. 1.67 × 10^-24

The atomic number of an element represents the number of protons in its nucleus, which is always a whole number. Other properties like atomic weight are generally not whole numbers due to isotopic variations.

Hence, the correct answer is option d. atomic number

The azimuthal quantum number (also known as the angular momentum quantum number, denoted by ‘l’) determines the shape of the orbital. For example, l=0 represents an s-orbital (spherical shape), l=1 represents a p-orbital (dumbbell shape), and so on

Hence, the correct answer is option b. Shape of the orbital

As the temperature of pure water increases, the dissociation of water molecules into H+ and OH- ions increases. This leads to a decrease in pH (indicating more H+ ions) and a corresponding decrease in pOH (indicating more OH- ions). Since the product of pH×pOH remains constant, both pH and pOH decrease with temperature.

Hence, the correct answer is option d. both pH and p O H decreases

Ionization potential refers to the energy required to remove the outermost electron from an atom. Neon (Ne) is a noble gas with a completely filled electron shell, making it highly stable. Therefore, it has the highest first ionization energy compared to Mg, Cl, and Na, which have more loosely bound outer electrons.

Hence, the correct answer is option a. Ne

Sodium sulfate (Na2SO4) is a salt derived from a strong acid (sulfuric acid) and a strong base (sodium hydroxide). When it dissolves in water, it does not hydrolyze and thus, the solution remains neutral. The other salts listed come from either weak acids or bases, which would cause the solution to be either acidic or basic.

Hence, the correct answer is option a. Na2​SO4​

For a first-order reaction, the time required to complete a certain percentage of the reaction is calculated using the half-life. After the first 50 minutes (one half-life), the reaction is 50% complete. To reach 75%, an additional half-life (another 50 minutes) is required. Thus, it takes a total of 100 minutes to reach 75% completion.

Hence, the correct answer is option b. 100 minutes

Malachite is a copper carbonate hydroxide mineral, Cu2(CO3)(OH)2​. It is one of the ores used for the extraction of copper.

Hence, the correct answer is option c. Cu

In the blast furnace, iron(III) oxide (Fe2O3​) is reduced to iron by carbon monoxide (CO). The carbon monoxide is generated in the furnace by the combustion of coke (a form of carbon) with oxygen from the air. The reaction is:

Fe2​O3​+3CO→2Fe+3CO2​

This reaction shows that carbon monoxide reduces the iron ore to produce metallic iron and carbon dioxide. Neither silica, coal, nor limestone directly reduce iron oxide in the blast furnace process. Limestone is added as a flux to remove impurities in the form of slag.

Hence, the correct answer is option d. CO

When equal volumes of 1.0 M HCl and 1.0 M NaOH are mixed together, they undergo a neutralization reaction to form water (H2O) and sodium chloride (NaCl). The balanced chemical equation for this reaction is:

HCl + NaOH → H2O + NaCl

Since the volumes and molarities of the reactants are equal, the reaction will go to completion, and all of the HCl and NaOH will be consumed.

The stoichiometry of the reaction is 1:1, meaning that for every 1 mole of HCl, 1 mole of NaOH is required to produce 1 mole of NaCl.

Let’s assume that we have V liters of each solution. The number of moles of HCl and NaOH in each solution can be calculated as follows:

Moles of HCl = Molarity × Volume = 1.0 M × V L = V moles
Moles of NaOH = Molarity × Volume = 1.0 M × V L = V moles

Since the reaction is 1:1, all of the HCl and NaOH will react to form V moles of NaCl.

The total volume of the resulting solution will be 2V liters (V liters of HCl solution + V liters of NaOH solution).

The concentration of NaCl in the resulting solution can be calculated as follows:

Concentration of NaCl = Moles of NaCl / Total Volume
Concentration of NaCl = V moles / 2V L
Concentration of NaCl = 0.5 M

So, the concentration of NaCl produced in the resulting solution will be 0.5 M.

Hence, the correct answer is option b. 0.5 M

In the contact process for manufacturing sulfuric acid, sulfur dioxide (SO₂) is oxidized to sulfur trioxide (SO₃) using a catalyst. The catalyst commonly used is vanadium(V) oxide (V₂O₅). This catalyst is preferred because it has a high efficiency at the operating temperatures of the process and does not deactivate quickly.

Hence, the correct answer is option d. V₂O₅

Molecularity refers to the number of reactant molecules involved in an elementary reaction. For the given reaction 2A+B→C+D, the molecularity is the sum of the coefficients of the reactants in the balanced equation. Here, there are 2 molecules of A and 1 molecule of B, making the molecularity 3.

Hence, the correct answer is option d. 3.0

Heavy water is water where the hydrogen atoms are replaced by deuterium, an isotope of hydrogen with an additional neutron. The chemical formula for heavy water is D₂O, where “D” stands for deuterium.

Hence, the correct answer is option a. Deuterium oxide(D₂O)

Galvanizing is the process of coating iron or steel with a layer of zinc to prevent rusting. The zinc layer protects the metal from corrosion by acting as a barrier and also by sacrificial protection, as zinc is more reactive than iron.

Hence, the correct answer is option d. Galvanizing

Sodium bicarbonate (NaHCO₃) and sodium hydroxide (NaOH) cannot coexist in solution because NaOH is a strong base and will react with NaHCO₃, a weak acid, to form sodium carbonate (Na₂CO₃) and water, effectively neutralizing the bicarbonate.

Hence, the correct answer is option a. NaHCO₃ and NaOH

Benzene exhibits resonance, where the electrons are delocalized over the carbon atoms, leading to the equalization of bond lengths. This resonance creates a structure where all C-C bonds in benzene are of the same length, intermediate between a single and a double bond.

Hence, the correct answer is option d. Resonance

Picric acid, chemically known as 2,4,6-trinitrophenol, does not contain a carboxylic acid (-COOH) group. Instead, it has a hydroxyl group (-OH) attached to a benzene ring with three nitro groups (-NO₂).

Hence, the correct answer is option d. Picric acid

primary amines react with acid (NaNO2+HCl) to form alcohol as major product.

Hence, the correct answer is option a. Alcohol

The Cannizzaro reaction involves the disproportionation of an aldehyde that does not have an alpha hydrogen, where one molecule is reduced to an alcohol, and the other is oxidized to a carboxylic acid.

Hence, the correct answer is option c. Cannizzaro reaction

Nitration of benzene is an electrophilic substitution reaction where a nitronium ion (NO₂^+​) acts as the electrophile and substitutes one hydrogen atom on the benzene ring to form nitrobenzene.

Hence, the correct answer is option b. Electrophilic substitution

The antiseptic action of Dettol is primarily due to Chloroxylenol, which is the active ingredient in Dettol. It has broad-spectrum antimicrobial properties, making it effective against a range of bacteria and fungi.

Hence, the correct answer is option d. Chloroxyenol

DDT (Dichlorodiphenyltrichloroethane) is a well-known synthetic insecticide. It was widely used in agriculture and for controlling mosquito populations, although its use has been restricted or banned in many countries due to environmental and health concerns.

Hence, the correct answer is option a. insecticide

A zwitterion is a molecule that contains both positive and negative charges but is overall electrically neutral. Glycine, an amino acid, can form a zwitterion in solution. Glycine hydrochloride specifically forms a zwitterion with a positive charge on the amine group (-NH₃⁺) and a negative charge on the carboxyl group (-COO⁻).

Hence, the correct answer is option d. Glycine hydrochloride

Fructose is a monosaccharide with a ketone group, making it a ketose. Unlike glucose, which is an aldose, fructose has a ketone functional group at the second carbon atom in its structure.

Hence, the correct answer is option b. Ketose

The rate constant (k) for a first-order reaction has units of time⁻¹, specifically seconds⁻¹ (sec⁻¹). This is because, in a first-order reaction, the rate of reaction is directly proportional to the concentration of one reactant, leading to the rate law Rate=k[A], where [A] is concentration and k is the rate constant with units of sec⁻¹.

Hence, the correct answer is option a. sec⁻¹

I promise that I won’t Let down to anyone.

It means to disappoint or fail someone.

Hence, the correct answer is option d. Let down

None of the options fit perfectly, but “passed on” can mean to die, which doesn’t fit the context of fainting. The correct expression should be “passed out,” meaning to lose consciousness due to the heat and stuffiness. However, from the given choices, “passed on” is the closest, though not entirely accurate.

Hence, the correct answer is option a. Passed on

“Tied down” means to feel restricted or confined. The speaker doesn’t want the other person to feel restricted by their presence.

Hence, the correct answer is option a. tied down

“Shows up” means to appear or arrive, often unexpectedly, which fits the description of someone unpredictable.

“Shows up” means to appear or arrive, often unexpectedly, which fits the description of someone unpredictable.

Hence, the correct answer is option d. shows up

Hence, the correct answer is option d. shows up

“Call on” means to visit someone, so Mahesh is planning to visit in the evening, which is why the speaker advises not to go out.

Hence, the correct answer is option c. call on

“Magniloquent” refers to using high-flown, pompous language, which is synonymous with “inflated” speech.

Hence, the correct answer is option d. inflated

“Vivacious” means lively and full of energy. The opposite would be “depressed,” which means feeling low or lifeless.

Hence, the correct answer is option c. depressed

“Mendacious” means lying or untruthful. The opposite is “veracious,” which means truthful.

Hence, the correct answer is option b. veracious

“Taciturn” describes a person who is reserved or speaks very little.

Hence, the correct answer is option a. tactium

The correct preposition after “cause” is “for” (as in “cause for concern”), and “take care of” is the correct expression meaning to look after something or someone.

Hence, the correct answer is option b. for ,of

“Sympathy for” is the correct phrase, meaning to feel pity or compassion towards someone. “Taste in” refers to one’s preference or liking for something, such as music.

Hence, the correct answer is option b. for ,in

“Contrary to” means in opposition to something, and “deaf ear to” is an idiom meaning to ignore or not listen to something.

Hence, the correct answer is option d. to, to

“Addicted to” means having a strong dependence on something, and “anxious to” means worried or concerned about something.

Hence, the correct answer is option b. to, to

“Touches upon” means to mention or briefly discuss a subject, and “turn into” means to transform something into something else, in this case, transforming a subject into a poem.

Hence, the correct answer is option b. upon, into

“Claustrophobia” is the fear of being in confined or enclosed spaces.

Hence, the correct answer is option c. claustrophobia

“Magnum opus” is a Latin term meaning a great or important work, typically the most significant achievement of an artist, writer, or composer.

Hence, the correct answer is option b. a great work

“Uxoricide” refers to the act of killing one’s wife.

Hence, the correct answer is option a. uxoricide

An “apiary” is a place where bees are kept, and an “aquarium” is a tank or enclosure where fish are kept.

Hence, the correct answer is option b. apiary , aquarium

The phrase “swear like a trooper” means to use profane or vulgar language very often.

Hence, the correct answer is option c. use swear words frequently

The idiom “as right as rain” means to be in perfect health or in excellent condition both emotionally and physically.

Hence, the correct answer is option a. One in the best emotional and physical condition

“Serve time” or “do time” is an idiom that means to spend time in prison as a punishment for a crime.

Hence, the correct answer is option b. be in prison / serve a prison sentence

“Call it a night” means to stop doing something, usually work or an activity, because it’s late and it’s time to rest or go to bed.

Hence, the correct answer is option c. stop some activity, work etc. to go to bed

“Play it by ear” means to act without a plan, adapting to the situation as it unfolds rather than following a fixed plan

Hence, the correct answer is option d. act according to the situation

“Be in the red” refers to being in debt or having a negative balance in a bank account, meaning you owe money.

Hence, the correct answer is option b. have no money in one’s bank account , owe
money to the bank

The correct indirect speech for “He said, ‘Congratulations'” is “He congratulated me.” This properly conveys the action of congratulating in reported speech

Hence, the correct answer is option b. He congratulated me.

a/b, a, b ∈ R, is equal to zero if a=0 and b≠0

Hence, the correct answer is option c. a=0,b≠0

x≥5 hence then value of x=6 which is greater than 6

Hence, the correct answer is option b. 6

|x-2| = 5

We know that modulus represent -ve & +ve sign

Taking -ve sign;

-(x-2)=5

or, -x+2=5

or, -x = 5-2

or, -x = 3

∴x= -3

again taking +ve sign

+(x-2)=5

or, x= 5+2

x=7

∴ x = -3 & 7

Hence, the correct answer is option d. {-3,7}

Given,

R = {(1, 2), (2, 3), (3,4)}

For Range={2,3,4}

For Domain={1,2,3}

Hence, the correct answer is option c. {2,3,4}

8a + 4, 6a – 2 and 3a + 7

We know A.P =>  b= (a+c)/2

then,

(6a-2)=(8a+4+3a+7)/2

12a -14 = 11a +1

a=11+4

a=15

Hence, the correct answer is option a. 15

Given,

(1 − ω +ω^2)³

we know, (1 + ω +ω^2)=0

1 + ω^2  = -ω

then,

(1+ω^2 − ω )³

=(-ω− ω )³

=(−2 ω )³

=(−2)³ x (ω )³

= -8 x 1 [ ∴(ω )³ =1 ]

= -8

Hence, the correct answer is option b. -8

Given the roots are 3 and 4

from the given options

put these value in option

Option a . x^2 -7x-12=0

put x=3;(3)^2-7×3-12=0

9-21-12≠0

option b.

Put x=3;(3)^2-7×3+12=0

9-21+12=0

0=0

Again,

Put x=4;(4)^2-7×4+12=0

16-28+12=0

0=0

Hence, the correct answer is option b.

Given,

𝑘𝑦^2 +(2 – 𝑘)^2 𝑥𝑦 – 3𝑥^2 = 0 comparing with ax^2 + 2hxy + by^2=0

a= -3, b=k,    2h = (2-k)^2 => h=(2-k)^2 / 2

For perpendicular,

a+b=0

-3+k=0

k= -3

Hence, the correct answer is option b. -3

Given,

𝑥^2 +𝑦^2 = 5 at (2, 1)

From option put the value of (x,y)=(2,1) in option

option a. 2x+y=5

2×2+1=5

5=5

Hence, the correct answer is option a

x² with respect to −𝑥^2

then, ( x² ) / (−𝑥^2) = -1

Hence, the correct answer is option d. -1